Daily Archives: December 4, 2012

並聯電阻

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這段改編自 2010 年 6 月 8 日的對話。

計算並聯電路（parallel circuit）等價電阻（equivalent resistance）的公式是

1/R = 1/R_1 + 1/R_2

但是，除非有三個或以上的電阻，否則，千萬不要用這一個版本，因為運算太繁複。步驟越多，時間就越長，而犯錯的機會亦會越大。簡言之，費時失事也。

你應改為使用高速版：

R = R_1 R_2 / (R_1 + R_2)

這版本的背誦亦不難，只要你記住「相乘除以相加」便行。

— Me@2012.12.04

2012.12.04 Tuesday (c) All rights reserved by ACHK

Godel 6

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This theorem implies that the only way a language can be incomplete is [that] there is a model of the language in which a particular statement is true, and another in which the statement is false.

For example, we can see that [for] the language [comprising] the symbols 0, 1, +, -, and , [] the statement []   is true [] if we take the structure to be C or R, but not if we choose Q. So it is clear that the formula a*a = 2 is not true in every model of the language and the thus the language is incomplete.

What the completeness theorem asserts is that this is the only way that a theory (set of formulas) can be incomplete and that every formula that satisfies every structure is provable in the language.

— Godel’s Completeness And Incompleteness Theorems

— Ben Chaiken

2012.12.04 Tuesday ACHK